Problem: $A$ $B$ $C$ If: $ AC = 80$, $ BC = 8x + 6$, and $ AB = 4x + 2$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 2} + {8x + 6} = {80}$ Combine like terms: $ 12x + 8 = {80}$ Subtract $8$ from both sides: $ 12x = 72$ Divide both sides by $12$ to find $x$ $ x = 6$ Substitute $6$ for $x$ in the expression that was given for $BC$ $ BC = 8({6}) + 6$ Simplify: $ {BC = 48 + 6}$ Simplify to find ${BC}$ : $ {BC = 54}$